ELEC6252 Future Wireless Techniques
MIMO Coursework
Submission Details
This assignment forms your second assessment for the “ELEC6252 Future Wireless Techniques”
and contributes 15% of your mark for the module.
You are required to produce a report, which needs to include the explanation of the designs and
implementation requested in the questions as well as Matlab code, figures, calculations that are
directly requested in the questions below. It is suggested that in the report you use the same
section order as in this document to describe the principles/designs/implementations/results
of the different schemes considered. Each figure in your write-up should have well labelled axes
and a relevant title or legend that identifies which signals/systems are shown. Although you
may verbally discuss your ideas with your classmates, you should not show them your Matlab
code, figures, calculations or text.
When you are finished, you need to submit your report and Matlab code electronically at
“https://handin.ecs.soton.ac.uk/handin/2122/ELEC6252/2/”
before 4pm on Friday 20/05/2022.
The marks distribution for each question is shown next to the question number below, where
the marks add up to 15.
If you notice any mistakes in this document or have any queries about it, please email me at
meh@ecs.soton.ac.uk.
Mohammed El-Hajjar
Learning Outcomes
1. Understand the concept of MIMO communications;
2. Investigate the design criteria for uplink and downlink communications;
3. Simulate and analyse various uplink and downlink decoders and precoders in multi-user
MIMO communications;
4. Produce high quality technical writing such as reports and reviews.
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Table 1: Marking Scheme
Accuracy of results: Are the obtained results correct? Is the formulation
correct? Are the plots accurate? Do you include all required plots?
50%
Interpretation of results: How well are the questions posed in the assignment
answered? Do you answer all parts of the questions? Do you include the
required derivations? Do you explain your derivations when requested?
30%
Presentation of results: How well are the designs explained, the plots labelled
and their contents discussed? Do you include all correct labels? Do you use
the right label units? Do you explain your results when requested?
20%
1 Multi-user MIMO System
Consider a multi-user multiple-input multiple-output (MIMO) system shown in Figure 1, where
a base station (BS) equipped with N antennas is communicating with K number of users. User
i, where i ∈ [1, K], is equipped with Nui antennas. In this coursework, assume all users have
the same number of antennas Nu .
Figure 1: Multi-user MIMO communications model.
There are two different scenarios for the configuration of Figure 1: uplink (UL) and downlink
(DL) scenarios. In the UL scenario, all or some of the K users are transmitting to the BS
at the same time, where the BS is required to decode the signals of all users. On the other
hand, in the DL scenario, the BS encodes the data for all communicating users and broadcasts
the signal, where each user is then required to decode its own signal. This multi-user MIMO
configuration exploits the unique, user-specific “spatial signature” of the individual users for
differentiating amongst them.
1.1 Uplink Communications [5 marks]
Consider K independent users in the UL multi-user MIMO system, where the BS and each
user equipment are equipped with N and Nu antennas, respectively. Figure 2 shows the uplink
channel, known as a multiple access channel (MAC) for K independent users. Let xu of size
2
Figure 2: UL channel model for multi-user MIMO system.
(Nu×1) and y of size (N×1) denote the transmitted signal from the u-th user, u = 1, 2, · · · , K
and the received signal at the BS, respectively. The channel gain between the u-th user and
the BS is represented by HULu of size (N ×Nu).
The received signal can be expressed as:
y = HUL1 x1 +H
UL
2 x2 + · · ·+HULK xK + z
=
[
HUL1 H
UL
2 · · · HULK
]

x1
x2
·
· · ·
· · ·
xK
+ z = H
UL

x1
x2
·
· · ·
· · ·
xK
+ z, (1)
where z is the additive White Gaussian noise (AWGN) with power spectral density of N0.
Question:
In this part of the coursework, we consider K = 4 users each having a Nu = 1 antennas
communicating with a BS equipped with N = 4 antennas. All users are using Quadrature Phase
Shift Keying (QPSK) modulation and transmitting over a Rayleigh-distributed narrowband
fading channel. You are required to implement the transmitter and receiver for this system
using Matlab, where you can assume perfect channel knowledge at the BS receiver. For the
receiver you are required to implement the following detectors:
1. Zero forcing (ZF) detector;
2. Maximum likelihood (ML) detector.
In your write-up, explain how the detector works using Equation (1) and include your Matlab
code and explain it. Also, produce a bit error ratio (BER) versus signal-to-noise ratio (SNR)
curve for each of the detectors shown on the same plot, which should be included in your
write-up. In your write-up you should also write your observations on the difference between
the detectors in terms of performance and complexity.
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Figure 3: DL channel model for multi-user MIMO system.
1.2 DL communications [5 Marks]
Figure 3 shows the DL channel model, where x is the transmit signal vector from the BS to all
K users of size (N × 1) and yu is the received signal at the u-th user, u = 1, 2, · · · , K of size
(Nu × 1). In Figure 3, HDLu represents the MIMO channel between the BS and the u-th user
of size (Nu ×N).
In a multi-user MIMO scenario, the received signal at the u-th user can be expressed as:
yu = H
DL
u x+ zu, u = 1, 2, · · · , K,
where zu represents the AWGN with power spectral density of N0 at the u-th user.
We can represent all user’ signals using a single vector as follows:
y1
y2
·
· · ·
· · ·
yK
 =

HDL1
HDL2
·
· · ·
· · ·
HDLK
x+

z1
z2
·
· · ·
· · ·
zK
 .
The u-th user is expected to detect its own data from the received signal yu. The main challenge
in this case is the coordinated signal detection on the receiver side, and hence transmitter
preprocessing is employed at the transmitter in order to simplify the decoding process at the
user equipment. In this part of the coursework, you are expected to implement the “channel
inversion” preprocessing method.
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1.2.1 Channel inversion
In this part, consider a BS employing N = 4 transmit antennas and K = 4 users, each using
Nu = 1 antenna. Hence, we can model the received signal at the u-th user as:
yu = H
DL
u

x1
x2
·
· · ·
· · ·
xk
+ zu, u = 1, 2, · · · , K. (2)
Note here that yu, xu and zu are scalar and not vectors.
Similarly, the received signals for all users can be represented as:
y1
y2
·
· · ·
· · ·
yK
 =

HDL1
HDL2
·
· · ·
· · ·
HDLK


x1
x2
·
· · ·
· · ·
xk
+

z1
z2
·
· · ·
· · ·
zK
 = HDLx+ z.
In order to cancel the interference at the u-th user imposed by the transmission of all users’
data, precoding or transmit preprocessing can be employed at the BS before the transmission of
the data so that the decoding process at the u-th user is simplified. In this case, it is expected
that the transmitter has information about the channel state information. In your simulation,
assume the transmitter has perfect channel knowledge.
When preprocessing is employed, the transmitter applies some processing prior to transmission,
which can be modelled as:
xˆ = Wx,
where W is the preprocessing weight matrix used to eliminate the multi-user interference at
the user equipment. In this question, consider using a zero forcing (ZF) preprocessor, which is
also referred to as channel inversion.
Question:
You are required to write a Matlab code that implements the channel inversion preprocessing
in the DL scenario employing N=4 transmit antennas, K=4 users with Nu=1 and BPSK
modulation. You are expected to explain your understanding of how the preprocessing works
and include a BER versus SNR results of your simulation. Also, you are expected to explain
your result and compare it with those results obtained for the UL scenario in Section 1.1.
Note here that you should maintain a normalised transmit power of 1. Hence, you might have
to normalise the transmit signal after preprocessing before transmission.
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2 Spatial Modulation [5 marks]
In this question you are required to simulate, a Spatial Modulation (SM) MIMO system em-
ploying 4 transmit antennas and 2 receive antennas and using BPSK modulation. The antennas
at the transmitter and receiver are spatially separated so that the channel coefficients between
each transmit and each receive antenna are independent. Also, consider a Rayleigh-distributed
narrowband fading channel, where the receiver has a perfect channel knowledge.
Question:
In this part you are expected to simulate the above system and employ maximum likelihood
detection, where you should produce BER versus SNR curves and then include the results
and Matlab code in your write-up. Also, you should comment on the SM advantages and
challenges and also compare the complexity of the SM detector with those detectors employed
in Section 1.1.
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